As Pew reports, public opinion has changed little since March 2012, when Pew first asked the question. Pew adds:

"The latest national survey by the Pew Research Center, conducted June 12-16 among 1,512 adults, finds a major factor in overall attitudes about Syria is the impression that the U.S. military is already stretched thin. About two-thirds (68%) say the U.S. is too overcommitted to get involved in another conflict, and just 27% disagree. The public also has questions about the opposition groups in Syria: 60% say that they may be no better than the current government."

"At the same time, the public does not reject a key argument for involvement in Syria: by a 53%-36% margin, most agree that it is important for the U.S. to support people who oppose authoritarian regimes."

The poll also found that most Americans don't have much interest in Syria.

"Just 15 percent say they are following news about charges that Syria has used chemical weapons against anti-government groups very closely, far fewer than are following other stories such as the government's collection of communication information (35 percent) and news about the national economy (30 percent). In fact, 33% say they are following news about Syria not at all closely," Pew found.